Find $\int {\arcsin x\,{\text{d}}x}$

attempt at integration by parts with $u = \arcsin x$ and $v' = 1$     M1

$\int {\arcsin x\,{\text{d}}x}  = x\arcsin x - \int {\frac{x}{{\sqrt {1 - {x^2}} }}{\text{d}}x} {\text{ }}$    A1A1

Note:     Award A1 for $x\arcsin x$ and A1 for $- \int {\frac{x}{{\sqrt {1 - {x^2}} }}{\text{d}}x}$.

solving $\int {\frac{x}{{\sqrt {1 - {x^2}} }}{\text{d}}x}$ by substitution with $u = 1 - {x^2}$ or inspection     (M1)

$\int {\arcsin x{\text{d}}x} = x\arcsin x + \sqrt {1 - {x^2}} + c$   A1

[5 marks]